Changes in doc/groups.dox [326:d3a7603026a2:325:1e2d6ca80793] in lemon-1.0
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doc/groups.dox
r326 r325 41 41 some graph features like arc/edge or node deletion. 42 42 43 Alteration of standard containers need a very limited number of 44 operations, these together satisfy the everyday requirements. 45 In the case of graph structures, different operations are needed which do 46 not alter the physical graph, but gives another view. If some nodes or 47 arcs have to be hidden or the reverse oriented graph have to be used, then 48 this is the case. It also may happen that in a flow implementation 49 the residual graph can be accessed by another algorithm, or a node-set 50 is to be shrunk for another algorithm. 51 LEMON also provides a variety of graphs for these requirements called 52 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only 53 in conjunction with other graph representations. 54 43 55 You are free to use the graph structure that fit your requirements 44 56 the best, most graph algorithms and auxiliary data structures can be used … … 46 58 47 59 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts". 60 */ 61 62 /** 63 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs 64 @ingroup graphs 65 \brief Graph types between real graphs and graph adaptors. 66 67 This group describes some graph types between real graphs and graph adaptors. 68 These classes wrap graphs to give new functionality as the adaptors do it. 69 On the other hand they are not light-weight structures as the adaptors. 48 70 */ 49 71 … … 134 156 135 157 /** 158 @defgroup matrices Matrices 159 @ingroup datas 160 \brief Two dimensional data storages implemented in LEMON. 161 162 This group describes two dimensional data storages implemented in LEMON. 163 */ 164 165 /** 136 166 @defgroup paths Path Structures 137 167 @ingroup datas … … 185 215 186 216 /** 217 @defgroup max_flow Maximum Flow Algorithms 218 @ingroup algs 219 \brief Algorithms for finding maximum flows. 220 221 This group describes the algorithms for finding maximum flows and 222 feasible circulations. 223 224 The maximum flow problem is to find a flow between a single source and 225 a single target that is maximum. Formally, there is a \f$G=(V,A)\f$ 226 directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity 227 function and given \f$s, t \in V\f$ source and target node. The 228 maximum flow is the \f$f_a\f$ solution of the next optimization problem: 229 230 \f[ 0 \le f_a \le c_a \f] 231 \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv} 232 \qquad \forall u \in V \setminus \{s,t\}\f] 233 \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f] 234 235 LEMON contains several algorithms for solving maximum flow problems: 236 - \ref lemon::EdmondsKarp "Edmonds-Karp" 237 - \ref lemon::Preflow "Goldberg's Preflow algorithm" 238 - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees" 239 - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees" 240 241 In most cases the \ref lemon::Preflow "Preflow" algorithm provides the 242 fastest method to compute the maximum flow. All impelementations 243 provides functions to query the minimum cut, which is the dual linear 244 programming problem of the maximum flow. 245 */ 246 247 /** 248 @defgroup min_cost_flow Minimum Cost Flow Algorithms 249 @ingroup algs 250 251 \brief Algorithms for finding minimum cost flows and circulations. 252 253 This group describes the algorithms for finding minimum cost flows and 254 circulations. 255 */ 256 257 /** 258 @defgroup min_cut Minimum Cut Algorithms 259 @ingroup algs 260 261 \brief Algorithms for finding minimum cut in graphs. 262 263 This group describes the algorithms for finding minimum cut in graphs. 264 265 The minimum cut problem is to find a non-empty and non-complete 266 \f$X\f$ subset of the vertices with minimum overall capacity on 267 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an 268 \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum 269 cut is the \f$X\f$ solution of the next optimization problem: 270 271 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} 272 \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f] 273 274 LEMON contains several algorithms related to minimum cut problems: 275 276 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut 277 in directed graphs 278 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to 279 calculate minimum cut in undirected graphs 280 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all 281 pairs minimum cut in undirected graphs 282 283 If you want to find minimum cut just between two distinict nodes, 284 please see the \ref max_flow "Maximum Flow page". 285 */ 286 287 /** 288 @defgroup graph_prop Connectivity and Other Graph Properties 289 @ingroup algs 290 \brief Algorithms for discovering the graph properties 291 292 This group describes the algorithms for discovering the graph properties 293 like connectivity, bipartiteness, euler property, simplicity etc. 294 295 \image html edge_biconnected_components.png 296 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth 297 */ 298 299 /** 300 @defgroup planar Planarity Embedding and Drawing 301 @ingroup algs 302 \brief Algorithms for planarity checking, embedding and drawing 303 304 This group describes the algorithms for planarity checking, 305 embedding and drawing. 306 307 \image html planar.png 308 \image latex planar.eps "Plane graph" width=\textwidth 309 */ 310 311 /** 312 @defgroup matching Matching Algorithms 313 @ingroup algs 314 \brief Algorithms for finding matchings in graphs and bipartite graphs. 315 316 This group contains algorithm objects and functions to calculate 317 matchings in graphs and bipartite graphs. The general matching problem is 318 finding a subset of the arcs which does not shares common endpoints. 319 320 There are several different algorithms for calculate matchings in 321 graphs. The matching problems in bipartite graphs are generally 322 easier than in general graphs. The goal of the matching optimization 323 can be the finding maximum cardinality, maximum weight or minimum cost 324 matching. The search can be constrained to find perfect or 325 maximum cardinality matching. 326 327 LEMON contains the next algorithms: 328 - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp 329 augmenting path algorithm for calculate maximum cardinality matching in 330 bipartite graphs 331 - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel 332 algorithm for calculate maximum cardinality matching in bipartite graphs 333 - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching" 334 Successive shortest path algorithm for calculate maximum weighted matching 335 and maximum weighted bipartite matching in bipartite graph 336 - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching" 337 Successive shortest path algorithm for calculate minimum cost maximum 338 matching in bipartite graph 339 - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm 340 for calculate maximum cardinality matching in general graph 341 - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom 342 shrinking algorithm for calculate maximum weighted matching in general 343 graph 344 - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching" 345 Edmond's blossom shrinking algorithm for calculate maximum weighted 346 perfect matching in general graph 347 348 \image html bipartite_matching.png 349 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth 350 */ 351 352 /** 187 353 @defgroup spantree Minimum Spanning Tree Algorithms 188 354 @ingroup algs … … 191 357 This group describes the algorithms for finding a minimum cost spanning 192 358 tree in a graph 359 */ 360 361 /** 362 @defgroup auxalg Auxiliary Algorithms 363 @ingroup algs 364 \brief Auxiliary algorithms implemented in LEMON. 365 366 This group describes some algorithms implemented in LEMON 367 in order to make it easier to implement complex algorithms. 368 */ 369 370 /** 371 @defgroup approx Approximation Algorithms 372 @ingroup algs 373 \brief Approximation algorithms. 374 375 This group describes the approximation and heuristic algorithms 376 implemented in LEMON. 377 */ 378 379 /** 380 @defgroup gen_opt_group General Optimization Tools 381 \brief This group describes some general optimization frameworks 382 implemented in LEMON. 383 384 This group describes some general optimization frameworks 385 implemented in LEMON. 386 */ 387 388 /** 389 @defgroup lp_group Lp and Mip Solvers 390 @ingroup gen_opt_group 391 \brief Lp and Mip solver interfaces for LEMON. 392 393 This group describes Lp and Mip solver interfaces for LEMON. The 394 various LP solvers could be used in the same manner with this 395 interface. 396 */ 397 398 /** 399 @defgroup lp_utils Tools for Lp and Mip Solvers 400 @ingroup lp_group 401 \brief Helper tools to the Lp and Mip solvers. 402 403 This group adds some helper tools to general optimization framework 404 implemented in LEMON. 405 */ 406 407 /** 408 @defgroup metah Metaheuristics 409 @ingroup gen_opt_group 410 \brief Metaheuristics for LEMON library. 411 412 This group describes some metaheuristic optimization tools. 193 413 */ 194 414 … … 239 459 240 460 This group describes the tools for importing and exporting graphs 241 and graph related data. Now it supports the LEMONformat242 and the encapsulated postscript (EPS) format. 461 and graph related data. Now it supports the \ref lgf-format 462 "LEMON Graph Format", the \c DIMACS format and the encapsulated 243 463 postscript (EPS) format. 244 464 */ … … 304 524 @ingroup concept 305 525 \brief Skeleton and concept checking classes for maps 306 526 307 527 This group describes the skeletons and concept checking classes of maps. 308 528 */ … … 319 539 build the library. 320 540 */ 541 542 /** 543 @defgroup tools Standalone utility applications 544 545 Some utility applications are listed here. 546 547 The standard compilation procedure (<tt>./configure;make</tt>) will compile 548 them, as well. 549 */ 550
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